Rays from sun converge at a point 15 cm in front of a concave mirror. ...
Solution:
Given, Rays from sun converge at a point 15 cm in front of a concave mirror.
To find, the position of the object to get the image size equal to the object size.
Let's consider the below diagram for better understanding.
From the given information,
- The image is formed at the focus (F) of the concave mirror.
- The object distance (u) is to be found.
Using the mirror formula,
1/f = 1/v - 1/u
As the image is formed at the focus, v = f.
1/f = 1/f - 1/u
1/f = 1/f - 1/u
1/f = (u-f)/uf
uf = f(u-f)
u = f(u-f)/f
u = u-f
2f = u
Therefore, the object distance (u) should be twice the focal length (f) to get the image size equal to the object size.
Given that the image is formed at a distance of 15 cm from the mirror, which is the focal length (f) of the mirror.
Therefore, u = 2f = 2 x 15 cm = 30 cm.
Hence, the correct option is (a) 30 cm in front of the mirror.